Traveling Waves Solutions for Bistable Differential-Difference Equations with Periodic Diffusion

This is the published version, also available here: http://dx.doi.org/10.1137/S0036139999357113.We consider traveling wave solutions to spatially discrete reaction-diffusion equations with nonlocal variable diffusion and bistable nonlinearities. To find the traveling wave solutions we introduce an ansatz in which the wave speed depends on the underlying lattice as well as on time. For the case of spatially periodic diffusion we obtain analytic solutions for the traveling wave problem using a piecewise linear nonlinearity. The formula for the wave forms is implicitly defined in the general periodic case and we provide an explicit formula for the case of period two diffusion. We present numerical studies for time t=0 fixed and for the time evolution of the traveling waves. When t=0 we study the cases of homogeneous, period two, and period four diffusion coefficients using a cubic nonlinearity, and uncover, numerically, a period doubling bifurcation in the wave speed versus detuning parameter relation. For the time evolution case we also discover a detuning parameter dependent bifurcation in observed phenomena, which is a product of both the nonlocal diffusion operator and the spinodal effects of the nonlinearity

Spatially Discrete FitzHugh-Nagumo Equations

This is the published version, also available here: http://dx.doi.org/10.1137/S003613990343687X.We consider pulse and front solutions to a spatially discrete FitzHugh--Nagumo equation that contains terms to represent both depolarization and hyperpolarization of the nerve axon. We demonstrate a technique for deriving candidate solutions for the McKean nonlinearity and present and apply solvability conditions necessary for existence. Our equation contains both spatially continuous and discrete diffusion terms

Computation of Mixed Type Functional Differential Boundary Value Problems

This is the published version, also available here: http://dx.doi.org/10.1137/040603425.We study boundary value differential-difference equations where the difference terms may contain both advances and delays. Special attention is paid to connecting orbits, in particular to the modeling of the tails after truncation to a finite interval, and we reformulate these problems as functional differential equations over a bounded domain. Connecting orbits are computed for several such problems including discrete Nagumo equations, an Ising model, and Frenkel--Kontorova type equations. We describe the collocation boundary value problem code used to compute these solutions, and the numerical analysis issues which arise, including linear algebra, boundary functions and conditions, and convergence theory for the collocation approximation on finite intervals

Comparison of dot chromosome sequences from D. melanogaster and D. virilis reveals an enrichment of DNA transposon sequences in heterochromatic domains

BACKGROUND: Chromosome four of Drosophila melanogaster, known as the dot chromosome, is largely heterochromatic, as shown by immunofluorescent staining with antibodies to heterochromatin protein 1 (HP1) and histone H3K9me. In contrast, the absence of HP1 and H3K9me from the dot chromosome in D. virilis suggests that this region is euchromatic. D. virilis diverged from D. melanogaster 40 to 60 million years ago. RESULTS: Here we describe finished sequencing and analysis of 11 fosmids hybridizing to the dot chromosome of D. virilis (372,650 base-pairs) and seven fosmids from major euchromatic chromosome arms (273,110 base-pairs). Most genes from the dot chromosome of D. melanogaster remain on the dot chromosome in D. virilis, but many inversions have occurred. The dot chromosomes of both species are similar to the major chromosome arms in gene density and coding density, but the dot chromosome genes of both species have larger introns. The D. virilis dot chromosome fosmids have a high repeat density (22.8%), similar to homologous regions of D. melanogaster (26.5%). There are, however, major differences in the representation of repetitive elements. Remnants of DNA transposons make up only 6.3% of the D. virilis dot chromosome fosmids, but 18.4% of the homologous regions from D. melanogaster; DINE-1 and 1360 elements are particularly enriched in D. melanogaster. Euchromatic domains on the major chromosomes in both species have very few DNA transposons (less than 0.4 %). CONCLUSION: Combining these results with recent findings about RNAi, we suggest that specific repetitive elements, as well as density, play a role in determining higher-order chromatin packaging

A community-based validation study of the short-form 36 version 2 philippines (tagalog) in two cities in the philippines

10.1371/journal.pone.0083794PLoS ONE812-POLN

Compressed representation of a partially defined integer function over multiple arguments

In OLAP (OnLine Analitical Processing) data are analysed in an n-dimensional cube. The cube may be represented as a partially defined function over n arguments. Considering that often the function is not defined everywhere, we ask: is there a known way of representing the function or the points in which it is defined, in a more compact manner than the trivial one

The compound machinery of government: The case of seconded officials in the European commission

This article explores the compound machinery of government. Attention is directed toward decision making within the core executive of the European Union - the European Commission. The article studies seconded national civil servants (SNEs) hired on short-term contracts. The analysis benefits from an original and rich body of surveys and interview data derived from current and former SNEs. The decision-making dynamics of SNEs are shown to contain a compound mix of departmental, epistemic, and supranational dynamics. This study clearly demonstrates that the socializing power of the Commission is conditional and only partly sustained when SNEs exit the Commission. Any long-lasting effect of socialization within European Union's executive machinery of government is largely absent. The compound decision-making dynamics of SNEs are explained by (1) the organizational affiliations of SNEs, (2) the formal organization of the Commission apparatus, and (3) only partly by processes of resocialization of SNEs within the Commission

Measurement of the prompt J/psi and psi(2S) polarizations in pp collisions at sqrt(s) = 7 TeV

The polarizations of prompt J/psi and psi(2S) mesons are measured in proton-proton collisions at sqrt(s) = 7 TeV, using a dimuon data sample collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 4.9 inverse femtobarns. The prompt J/psi and psi(2S) polarization parameters lambda[theta], lambda[phi], and lambda[theta, phi], as well as the frame-invariant quantity lambda(tilde), are measured from the dimuon decay angular distributions in three different polarization frames. The J/psi results are obtained in the transverse momentum range 14 < pt < 70 GeV, in the rapidity intervals abs(y) < 0.6 and 0.6 < abs(y) < 1.2. The corresponding psi(2S) results cover 14 < pt < 50 GeV and include a third rapidity bin, 1.2 < abs(y) < 1.5. No evidence of large transverse or longitudinal polarizations is seen in these kinematic regions, which extend much beyond those previously explored

Measurement of the triple-differential cross section for photon plus jets production in proton-proton collisions at √s = 7 TeV

Peer reviewe

Evidence for the 125 GeV Higgs boson decaying to a pair of tau leptons

Peer reviewe